Reconfigurable antenna based solutions for device authentication and intrusion detection in wireless networks

ABSTRACT

Channel based authentication schemes for intrusion detection that operates at the physical layer are described that apply the capabilities of a pattern reconfigurable antenna for improved performance. Performance gains are achieved by the schemes as a function of the number of antenna modes. The first scheme relies on a channel based fingerprint for differentiating between transmitters whereas another scheme poses the intruder detection problem as a generalized likelihood ratio (GLR) test problem that operates on the channel realizations corresponding to different modes present in a reconfigurable antenna. The benefits of these two schemes over single element antennas are demonstrated. General guidelines are provided on how to choose the different elements of the decision metric in order to realize better performance for physical layer based authentication schemes based on any diversity scheme.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of U.S. application Ser. No. 14/343,244filed Jul. 24, 2014, which is the National Stage of InternationalApplication No. PCT/US2012/054205, filed Sep. 7, 2012, which claims thebenefit of U.S. Provisional Application No. 61/532,353, filed Sep. 8,2011 and U.S. Provisional Application No. 61/532,136, filed Sep. 8,2011, the disclosures of which are incorporated herein by reference intheir entireties.

STATEMENT OF FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Grant Nos. 0916480and 1028608 awarded by the National Science Foundation. The governmenthas certain rights in the invention.

TECHNICAL FIELD

The present invention relates generally to the field of multi-elementantenna systems. Specifically, the present invention relates to methodsfor device authentication and intrusion detection in MIMO systems usingmulti-element reconfigurable antennas.

BACKGROUND

Large scale proliferation of wireless technology coupled with theincreasingly hostile information security landscape is of seriousconcern. The fundamental broadcast nature of wireless data transmissionaggravates the situation since unlike wired networks it introducesmultiple avenues for attack and penetration into a network. Attacks onwireless networks have become increasingly sophisticated with theincreasing pervasiveness of these networks. It is challenging to detectand counteract intrusions in wireless networks due to the inherentbroadcast nature of the medium. Currently known security risks includedenial of service attacks, man-in-the-middle attacks, MAC addressspoofing attacks, client-to-client attacks, network injection and bruteforce attacks against access point passwords. Man-in-the-middle attacksand spoofing attacks pose a particularly significant intrusion threat towireless networks since such attacks allow intruders to hijack aconnection already established by a legitimate user. These risks willcontinue to increase in number and sophistication as wireless networksstart to carry increasingly more sensitive information.

Though advanced wireless intrusion protection and detection systems havebeen developed and deployed to mitigate such threats, it has beenrepeatedly demonstrated that each method has its point of failure and nosingle method guarantees protection against all attacks. See, e.g., W.A. Arbaugh, N. R. Shankar and Y. C. Justin Wan, “Your 802.11 WirelessNetwork has No Clothes,” IEEE Wireless Communications, pages 44-51,2001; N. Borisov, I. Goldberg, and D. Wagner, “Intercepting mobilecommunications: the insecurity of 802.11,” MobiCom '01: Proceedings ofthe 7th annual international conference on Mobile computing andnetworking, pages 180-189, New York, N.Y., USA, 2001: ACM. Also, whileseveral established protection mechanisms such as cryptography basedtechniques and wireless intrusion prevention systems exist, each methodhas its own weaknesses and is susceptible to failure under differentcircumstances. The resulting uncertainties have led to a significantparadigm shift in the design and implementation of wireless security inrecent times, where an increasingly cross-layer approach is beingpursued to protect wireless networks. One such avenue for security hasbeen to use the physical layer information to protect against intrudersand attackers. Especially channel information available at the physicallayer is being increasingly used to provide an additional degree ofprotection against intruders. The idea of using physical layerinformation to enhance security has been approached under two broadcategories. The first category of work focuses on cryptography basedtechniques that utilize physical layer information to generate and sharekeys. See, e.g., B. Azimi-Sadjadi, A. Kiayias, A. Mercado, and B. Yener,“Robust key generation from signal envelopes in wireless networks,” inCCS '07: Proceedings of the 14th ACM conference on Computer andcommunications security. New York, N.Y., USA: ACM, 2007, pp. 401-410; J.E. Hershey, A. A. Hassan, and R. Yarlagadda, “Unconventionalcryptographic keying variable management,” Communications, IEEETransactions on, 43(1):3-6, 1995; S. Jana, S. N. Premnath, M. Clark, S.K. Kasera, N. Patwari, and S. V. Krishnamurthy, “On the effectiveness ofsecret key extraction from wireless signal strength in realenvironments,” in Proceedings of the 15th annual internationalconference on Mobile computing and networking. New York, N.Y., USA: ACM,2009, pp. 321-332; and H. Kitaura, A. Sasaoka, “A scheme of private keyagreement based on the channel characteristics in OFDM land mobileradio,” Electronics and Communications in Japan Part 3: FundamentalElectronic Science, vol. 88, no. 9, pp. 1-10, 2005; N. Patwari, J.Croft, S. Jana, and S. K. Kasera, “High-Rate Uncorrelated Bit Extractionfor Shared Secret Key Generation from Channel Measurements. IEEETransactions on Mobile Computing, 9:17-30, 2009; and S. Yasukawa, H.Iwai, and H. Sasaoka, “Adaptive key generation in secret key agreementscheme based on the channel characteristics in OFDM,” Information Theoryand Its Applications, 2008, ISITA 2008, International Symposium on,pages 1-6, 2008. In the second approach, some form of the physical layerinformation associated with a device, such as channel frequency responseor RSSI, is used as an identifier to differentiate between differentdevices and thus provide a mechanism for authentication. See e.g., M.Demirbas and Y. Song, “An RSSI-based Scheme for Sybil Attack Detectionin Wireless Sensor Networks,” WOWMOM '06: Proceedings of the 2006International Symposium on World of Wireless, Mobile and MultimediaNetworks, pages 564-570, Washington, D.C., USA, 2006, IEEE ComputerSociety; D. B. Faria and D. R. Cheriton, “Detecting identity-basedattacks in wireless networks using signal prints,” in WiSe '06:Proceedings of the 5th ACM workshop on Wireless security. New York,N.Y., USA: ACM, 2006, pp. 43-52; N. Patwari and S. K. Kasera, “Robustlocation distinction using temporal link signatures,” in MobiCom '07:Proceedings of the 13th annual ACM international conference on Mobilecomputing and networking. New York, N.Y., USA: ACM, 2007, pp. 111-122;L. Xiao, L. Greenstein, N. Mandayam, and W. Trappe, “Fingerprints in theether: Using the physical layer for wireless authentication,” inCommunications, 2007. ICC '07. IEEE International Conference on, June2007, pp. 4646-4651; L. Xiao, L. Greenstein, N. Mandayam, and W. Trappe,“Using the physical layer for wireless authentication in time-variantchannels,” Wireless Communications, IEEE Transactions on,7(7):2571-2579, 2008; and “Channel-based spoofing detection infrequency-selective Rayleigh channels,” Wireless Communications, IEEETransactions on, vol. 8, no. 12, pp. 5948-5956, 2009.

Intrusion detection has traditionally been categorized into misusedetection or anomaly detection techniques. While the former usespatterns characteristic of known attacks to detect known intrusions, thelatter relies on detecting deviations from the established behaviorpatterns in the system. Y. Zhang and W. Lee, “Intrusion detection inwireless ad-hoc networks,” Proceedings of the 6th annual internationalconference on Mobile computing and networking in MobiCom '00, pages275-283, New York, N.Y., USA, 2000, ACM. In many usage scenarios, wherethe physical link remains unchanged over a session, the wireless channelresponse corresponding to the link can be considered to represent theestablished behavior pattern for that link. Any changes that violatethis pattern abruptly beyond a certain limit can be then checked foradversarial behavior.

In parallel to these developments, significant progress has been made inthe design of reconfigurable antennas resulting in numerous designs thatare reconfigurable in frequency, pattern, polarization or a combinationof these parameters. For many new and emerging high data rateapplications, pattern reconfigurable antennas are of special interestdue to their ability to generate highly uncorrelated radiation patternsthat can produce uncorrelated channel realizations in a multi-path richwireless medium for a given frequency. See, e.g., A. Forenza and J.Heath, R. W., “Benefit of pattern diversity via two-element array ofcircular patch antennas in indoor clustered MIMO channels,”Communications, IEEE Transactions on, vol. 54, no. 5, pp. 943-954, May2006. The ability of pattern reconfigurable antennas to enhance systemthroughput has been well demonstrated by D. Piazza, P. Mookiah, M.D'Amico, and K. R. Dandekar, “Experimental Analysis of Pattern andPolarization Reconfigurable Circular Patch Antennas for MIMO Systems,Vehicular Technology, IEEE Transactions on, 59(5):2352-2362, 2010. Suchantennas have gained widespread attention due to their ability toimprove throughput and are gradually finding their way into commercialwireless systems. The uncorrelated nature of the channel realizationsdue to such an antenna are believed by the inventors to hold greatpotential to enhance physical layer based security schemes.

Previous works that explored the idea of physical layer informationbased authentication are based on the use of conventional antennas. Itis desired to demonstrate how the capabilities of reconfigurableantennas to generate decorrelated channels can be used to enhancephysical layer information based device authentication schemes forwireless systems. However, it should be noted that the security schemedescribed herein is not meant to be a replacement for existing higherlayer security algorithms. Instead, it is desired to leverage thecapabilities of reconfigurable antennas to provide an additional layerof security for wireless systems. Moreover, it is also desired todevelop a general guideline on how to choose the different elements ofthe decision metric in order to realize better performance for physicallayer based authentication schemes based on any diversity scheme.

The problem that is addressed by the invention is one of establishingthe identity of a transmitting device in a wireless network. Spoofingattacks in network security encompasses a wide range of attacks that arebased on one entity deceiving another to accept the attacking entity'sidentity to be something else. Many variants of this attack rely on theattacker monitoring the packet flow between the victims to obtain somesensitive information that identifies one or both of the victims.Information obtained thus serves as the launching pad for moresophisticated attacks. Due to the unbounded nature of the mediumemployed, such information can be obtained easily in a wireless networkmaking them especially vulnerable to such attacks. Hence, an additionalmechanism for protection at the physical layer that can detect intrusionand thwart such attacks can significantly enhance the security of awireless network. The present invention addresses these needs in theart.

SUMMARY

The invention addresses the above problems by providing a deviceauthentication scheme that utilizes the capabilities of reconfigurableantennas to provide a robust additional layer of security againstattacks that are based on spoofing transmitter identities as well asman-in-the-middle attacks. Wireless channel information is available tothe transmitter at the physical layer for channel equalization. Channelinformation corresponding to different modes in the reconfigurableantenna is combined to form a fingerprint for a legitimate transmitterduring the outset of the connection. Channel information correspondingto later transmissions from the transmitter is compared with thisfingerprint based on a test metric such as the angle between thefingerprint corresponding to the incoming transmission and fingerprintvalue stored in memory. The acceptable angle range between the twofingerprints is determined based on the acceptable false alarm rate.

The probability distribution function required to determine an adaptivethreshold for a given false alarm rate is computed during the connectioninitialization phase. Multiple training packets are transmitted from thelegitimate transmitter to the receiver and the test metric is computedbetween fingerprints corresponding to all the training packets. Thecomputed metrics are gathered to form the distribution function on themetric to determine the threshold for a given false alarm rate.

The method is most efficient when the different modes of themulti-element reconfigurable antenna are substantially decorrelated.Channel estimates for all the different modes may be obtained withoutdegrading throughput and power consumption by cycling respectiveantennas in the communication system through the modes during thetransmission of a data packet including training symbols, a payload, anda pad between the payload and training symbols. Preferably, the pad hasa duration long enough to permit the respective antennas to switch modeswhile a channel estimation is being performed for the respective modes.

The methods described herein show marked improvement in intruderdetection rates. Increasing the number of antenna modes used in thefingerprint improves detection rates linearly at low false alarm rates.Moreover, the method provides a precise guideline on how to choose areconfigurable antenna and the number of modes in order to achieve therequired level performance in a given environment. Enforcing security atthe lower layer provides a robust extra level of security and helps theupper level layers to better handle spoofing and man-in-the-middleattacks.

The invention further addresses the above problems by providingintrusion detection by monitoring the channel for any abrupt changes inits statistics through repeated applications of the generalizedlikelihood ratio (GLR) test. The scheme is based on the idea that thestatistics of the link corresponding to an intruder who is physicallylocated at a different location will be different from that of thelegitimate user and when the intruder tries to inject packets over thesame connection, it will trigger an abrupt change in the GLR value.Additionally, the invention utilizes a pattern reconfigurable antenna toimprove the performance of the intrusion detection scheme. By pickingantenna modes that are decorrelated in their radiation patterns,decorrelated channel realizations can be obtained to enhance systemperformance. Hence, channels corresponding to different modes of theantenna can be expected to have different statistics, a property whichis exploited to the benefit of the proposed detection scheme.

However, the use of reconfigurable antennas (pattern diversity) shouldbe differentiated from schemes that use multiple antennas (spatialdiversity) with perfect decorrelation between the elements. See, e.g.,L. Xiao, L. Greenstein, N. Mandayam, and W. Trappe, “MIMO-assistedchannel-based authentication in wireless networks,” Information Sciencesand Systems, 2008. CISS 2008. 42nd Annual Conference on, pages 642-646,2008; L. Xiao, L. Greenstein, N. Mandayam, and W. Trappe, “Using thephysical layer for wireless authentication in time-variant channels,”Wireless Communications, IEEE Transactions on, 7(7):2571-2579, 2008; L.Xiao, L. Greenstein, and N. B. Mandayam, and W. Trappe, “Channel-basedspoofing detection in frequency-selective Rayleigh channels” WirelessCommunications, IEEE Transactions on, 8(12):5948-5956, 2009. Thus, theinvention provides channel correlation between the different diversitybranches and specifically quantifies the effect of correlation ondetection performance. A reconfigurable antenna provides a morepractically viable solution to generate multiple channel realizationsthan spatially separated multiple antenna elements due to cost and spaceconstraints.

In many public open networks (e.g. coffee shops), higher levelauthentication solutions are usually not implemented. Freely availablesoftware tools such as Firesheep can be used to simply execute sessionhijacking attacks when users visit insecure websites in such networks. Awireless access point equipped with reconfigurable antennas that canimplement the proposed method can be used to provide a layer of securitythat can significantly alleviate such security threats in thesenetworks. In networks with higher level security mechanisms forencryption, authentication and integrity, the proposed scheme cancomplement those mechanisms while they continue to play their part insecuring the wireless link.

Accordingly, the invention further provides an intrusion detectionscheme that operates based on channel information available through areconfigurable antenna to protect a wireless link against variousattacks that are based on spoofing transmitter identities as well asman-in-the-middle attacks. Wireless channel information for thedifferent antenna modes will be available to the transmitter at thephysical layer for channel equalization purposes. In accordance with theinvention, the statistics of this channel information will show abruptchanges when intrusion occurs. The inventors have devised a generalizedlikelihood ratio test to repeatedly monitor the statistics of thechannel and raise an alarm when an abrupt change is detected. Thecumulative change observed in the cumulative statistics of the channelscorresponding to the multiple modes of a reconfigurable antennasignificantly strengthens the efficacy of the invention compared to atest that relies on the change of statistics corresponding to a fixedmode antenna.

The methods disclosed herein show marked improvement in intruderdetection rates. Increasing the number of antenna modes used in the GLRtest improves detection rates at low false alarm rates. Moreover, themethod provides precise guidelines on how to choose a reconfigurableantenna and the number of modes in order to achieve the required levelperformance in a given environment. The method of the invention providesa high rate of detection at low false alarm rates. It has been shownthat the performance can be increased significantly with the addition ofextra antenna modes. Enforcing security at the lower layer provides arobust extra level of security and helps the upper level layers tobetter handle spoofing and man-in-the-middle attacks.

Reconfigurable antennas are mainly incorporated in wireless devices fortheir ability to increase spectral efficiency. The techniques describedherein add significant additional value to the reconfigurable antenna inthe system since it is being employed for an additional purpose as well.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates different stages during the evolution of theauthentication problem during a data transfer session betweentransmitter T and receiver R that is monitored by an intruder I.

FIG. 2 illustrates the temporal variation in channel frequency responsefor a single link with a single antenna configuration over a period of 6hours.

FIG. 3 illustrates a CAD model of sample layout of a measurementenvironment for the indicated test locations of R, T, and I.

FIG. 4 illustrates radiation patterns of the LWA in the elevation plane(corresponding to the plane of the 2D model of FIG. 3) for 5 differentconfigurations where the patterns are vertically polarized for allmodes.

FIG. 5 illustrates pattern and channel correlation coefficients wherethe upper X axis corresponds to indices of antenna modes and lower Xaxis corresponds to indices of different frequencies. Correlations aredefined with respect to mode 1 and the first measured frequency,respectively.

FIG. 6 illustrates β as a function of a for pattern and frequencydiversity for N=2. (The remaining 7 pairs for pattern diversity followsimilar trends and were omitted to avoid clutter in the figure.)

FIG. 7 illustrates β as a function of a for reconfigurable antenna basedauthentication at different values of N.

FIG. 8 illustrates β as a function of α when the average correlationbetween different elements in ĥ remains the same with increasing N,where elements correspond to frequency points spaced at 5 MHz.

FIG. 9 illustrates realized false alarm rates as a function of designedfalse alarm rates during an online mode of operation.

FIG. 10 illustrates β as a function of realized α during onlineoperation. Solid lines correspond to 10 training packets and dashedlines correspond to 25 training packets.

FIG. 11 illustrates an extended transmit frame that can be used toobtain channel estimates for multiple antenna modes during a singlepacket transmission.

FIG. 12 illustrates the intruder problem addressed by the inventionwhereby in (a) I eavesdrops on a data transfer session between R and Tto obtain sensitive information about T's identity and uses theinformation in (b) to masquerade as T to R.

FIG. 13 illustrates a sample evolution of the GLR test where NT=25,NF=100, N=5, and M=1 for a threshold chosen to be the maximum of L(h)observed during training.

FIG. 14 illustrates radiation patterns corresponding to the 5 differentantenna modes in the elevation plane corresponding to the measurementenvironment plane shown in FIG. 3. All patterns are verticallypolarized.

FIG. 15 illustrates average DET curves for a single antenna (M=1) modefor different values of N, where ND is equal to N for each curve andNT=25. For a given α, β decreases with the block size; however, at low αlevels, the corresponding β levels remain unacceptably high for a singleantenna mode even at relatively large block sizes.

FIG. 16 illustrates CDF of P for different values of M showing that thesupport and mean shift toward higher values with increasing M.

FIG. 17 illustrates the variation of detection probability with ND for asingle antenna (M=1) mode at α=0.05 where NT=25 and ND is equal to N foreach curve. The dashed segments correspond to points where N_(D)<N.Longer delays result in only marginal improvements in detection. LargerN improves performance, but the minimum required detection delay islonger for larger N's.

FIG. 18 illustrates a variation of a with NF for a single antenna (M=1)mode at β=0.05, where NT=25 and N_(D) is equal to N for each curve.Longer numbers of transmissions from T increases the probability offalse alarms. Larger N improves performance due to better σ₀ estimates.

FIG. 19 illustrates average DET curves for multiple antenna modes forN=N_(D)=10 and NT=25. For a given α, β decreases with an increasingnumber of antenna modes. Acceptable levels of β can be achieved at low αlevels by using multiple antenna modes.

FIG. 20 illustrates the variation of detection probability with N_(D)for multiple antenna modes at α=0.05, N=N_(D)=10, and N_(T)=25. As inFIG. 17, longer delays result in only marginal improvements in detectionrates without requiring longer detection delays.

FIG. 21 illustrates variation of a with NF for multiple antenna modes atβ=0.05 and N_(T)=25, where N_(D)=N for each curve and a decreases withM.

FIG. 22 illustrates the average DET curves for different antenna modecombinations wherein N=N_(D)=10 and N_(T)=25. Detection rates have adirect correlation with the correlation coefficient between the patternsof the employed antenna modes. For a given M, lower correlationcoefficients between the antenna patterns result in better detection fora given α.

FIG. 23 illustrates the average DET curves for M=1 and M=5 for adifferent number of training samples where N=N_(D)=10. Solid linesindicate M=1 and dotted lines indicate M=5. Longer training results inbetter detection at lower α regions; however, the gains achieved frommore training cannot match the gains achieved by employing more numberof antenna modes.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention may be understood more readily by reference to thefollowing detailed description taken in connection with the accompanyingfigures and examples, which form a part of this disclosure. It is to beunderstood that this invention is not limited to the specific products,methods, conditions or parameters described and/or shown herein, andthat the terminology used herein is for the purpose of describingparticular embodiments by way of example only and is not intended to belimiting of any claimed invention. Similarly, any description as to apossible mechanism or mode of action or reason for improvement is meantto be illustrative only, and the invention herein is not to beconstrained by the correctness or incorrectness of any such suggestedmechanism or mode of action or reason for improvement. Throughout thistext, it is recognized that the descriptions refer both to methods andhardware/software for implementing such methods.

A detailed description of illustrative embodiments of the presentinvention will now be described with reference to FIGS. 1-23. Althoughthis description provides a detailed example of possible implementationsof the present invention, it should be noted that these details areintended to be exemplary and in no way delimit the scope of theinvention.

System Overview

The invention described herein addresses the dual problems ofauthentication and intrusion detection is wireless networks. As will beexplained below, the invention addresses these problems by providingmethods for device authentication and intrusion detection in MIMOsystems using multi-element reconfigurable antennas. While techniquesfor authentication and intrusion detection are described in differentembodiments for ease of description, those skilled in the art willappreciate that the respective methods and schemes described herein maybe combined into the same wireless transmission system as desired.

Authentication Scheme for Wireless Networks

The authentication scheme used in a first exemplary embodiment of theinvention is based on the basic idea that the channel between thelegitimate transmitter and receiver is difficult to replicate by amalicious entity. Different modes in a reconfigurable antenna presentdifferent views of this channel. As a result, emulating all the channelsseen by the different modes becomes a more difficult proposition for theintruder. Therefore, associating a device with a unique channel basedidentifier or fingerprint could yield a robust authentication mechanism.This identifier utilizes the raw complex channel information rather thanany abstracted power based metrics such as RSSI, which allows the schemeto be more robust to attacks that try to circumvent it through simplepower control. Moreover, the inventive method does not attempt tolocalize the transmitting device. Rather, the inventive method finds aunique identifier for each transmitting device in the network based onits location. A data packet that generates the proper locationfingerprint at the receiver can be then trusted to be arriving from thelegitimate user and vice versa.

The problem scenario consists of three different players: a receiver(R), a transmitter (T) and an intruder (I). In practice R couldcorrespond to a wireless access point while T and I correspond to twousers trying to connect to R. In practice, it is more likely that awireless access point would be equipped with a comprehensivereconfigurable antenna system due to space and cost constraints.Therefore, it is assumed that a reconfigurable antenna with N differentconfigurations is employed only at R with T and I equipped withconventional omni-directional antennas.

The problem evolves as shown in FIG. 1. As shown, T and R initiate aconnection at the outset of the session and are in the process ofexchanging information (FIG. 1(a)). At this stage, R measures and storesthe channel between itself and T for N different antenna modes. I startsmonitoring this exchange during this session until it obtains theidentifying information corresponding to T (FIG. 1(b)). After obtainingthis information, I tries to pose as T to mislead R (FIG. 1(c)). Thegoal is now to enable R to distinguish between T and I at the physicallayer based on the stored channel information. R makes this distinctionby comparing the estimated channels for the N antenna modes for theincoming packet with the most recent copy stored in memory (FIG. 1(d)).Based on the outcome of this test, R makes a decision on whether thepacket arrived from T or not. It is assumed that R performs thiscomparison periodically and holds the most recent copy of the channelinformation that passes the test in its memory for the next comparison.

Channel Model

Unlike mobile phone based services, a multitude of current and emergingwireless data services involve stationary terminals at both ends of thelink. The terminal locations are usually fixed or movements arelocalized to a very small area near the seated user for the duration ofa session. Temporal variations in such channels, termed as nomadicmobility channels, mostly arise due to movements of people and objectsin the vicinity of the terminals. The description herein is limited tosuch channels since they represent a more common usage scenario forcurrent high data rate applications.

For a fixed link, the directional channel impulse response for anenvironment with L clusters and K rays per cluster is given by:

$\begin{matrix}{{h\left( {\phi_{R},\phi_{\gamma}} \right)} = {\frac{1}{\sqrt{LK}}{\sum\limits_{l = 0}^{L - 1}{\sum\limits_{k = 0}^{K - 1}{\beta_{kl}{\delta\left( {\phi^{T} - \phi_{kl}^{T}} \right)}{\delta\left( {\phi^{T} - \phi_{kl}^{R}} \right)}}}}}} & (1)\end{matrix}$where ϕ^(T) and ϕ^(R) are the transmit and receive angles, β_(kl) is thecomplex ray gain of the kth ray in the lth cluster, and ϕ_(kl) ^(T) andϕ_(kl) ^(R) are their corresponding angles of departure and arrival. Thenarrowband channel impulse response corresponding to this cluster modelis given by:h=∫ _(−π) ^(π)∫_(−π) ^(π) G _(R)(ϕ^(R))h(ϕ_(R),ϕ_(T))G _(T)(ϕ^(T))dϕ^(T) dϕ ^(R)  (2)where G_(R)(ϕ^(R)) and G_(T)(ϕ^(T)) are the antenna gain patterns at thereceiver and transmitter, respectively. If it is assumed that anomni-directional radiation pattern is provided at the transmitter,substituting equation (1) in equation (2) simplifies to:

$\begin{matrix}{h = {\frac{1}{\sqrt{LK}}{\sum\limits_{l = 0}^{L - 1}{\sum\limits_{k = 0}^{K - 1}{\beta_{kl}{G_{R}\left( \phi_{kl}^{R} \right)}}}}}} & (3)\end{matrix}$For a sufficiently narrowband channel, flat fading can be assumed, and hwill be given by a single complex number with |h| distributed accordingto a Rayleigh or Ricean distribution. Equation (3) quantifies thedependence of h on the antenna configuration at the receiver. For thekth receiver antenna configuration G_(k)(ϕ^(R)), the correspondingchannel is denoted by h_(k).

Previous measurement campaigns on nomadic mobility channels have shownthat, for stationary terminals, the temporal channel variations areimparted primarily due to shadowing and scattering by the movingscatterers in the vicinity of the link. See, e.g., J. Medbo, J.-E. Berg,and F. Harrysson, “Temporal radio channel variations with stationaryterminal,” in Vehicular Technology Conference, 2004. VTC2004-Fall. 2004IEEE 60th, vol. 1, 2004, pp. 91-95; P. Pagani and P. Pajusco,“Characterization and modeling of temporal variations on anultrawideband radio link,” Antennas and Propagation, IEEE Transactionson, vol. 54, no. 11, pp. 3198-3206, 2006; and C. Oestges, D.Vanhoenacker-Janvier, and B. Clerckx, “Channel characterization ofindoor wireless personal area networks,” Antennas and Propagation, IEEETransactions on, vol. 54, no. 11, pp. 3143-3150, 2006. FIG. 2 shows thetemporal variation in the measured frequency response corresponding to asingle link for a single antenna mode. The entire shaded regionconstitutes the total power variation in the channel over a period ofapproximately 6 hours during regular working hours when there wasconsiderable human movement between the two ends of the link. Theresults follow similar trends that have been reported in earliermeasurements where most of the variations are confined to narrowregions. See Medbo et al. Consistent with the models proposed in theseearlier works, the channel may be modeled as follows:ĥ _(k) =Xh _(k) +∈+n  (4)where X denotes the shadowing imposed on the time invariant componenth_(k), ∈ is the additional small scale fading component induced by thescatterers, and n denotes receiver noise. ∈ and n can be modeled as acomplex Gaussian process with 0 means and variances σ_(∈) ² and σ_(N) ²respectively. X is modeled as a random variable with a log-normaldistribution with 0 mean and variance σ₅ ².Identification Metric and Identity Test

In order to perform the channel comparison, R would require anauthentication metric based on the channel information. The metriccorresponding to the two channel realizations can be then used to make adecision about the transmitter's identity. One can start with a decisionvector that is given by:ĥ=[|ĥ ₁ ||ĥ ₂ | . . . |ĥ _(N)|]^(T)  (5)where ĥ is a vector that consists of channel amplitudes corresponding todifferent receiver antenna modes. The vector ĥ can be considered as thespatial signature or fingerprint associated with a terminal at aparticular location. The angle between two spatial signatures ĥ_(i) andĥ_(l) in the N dimensional space is now proposed as the test statisticto test if the signatures correspond to the same terminals:

$\begin{matrix}{\theta = {\cos^{- 1}\left( \frac{{\hat{h}}_{i} - {\hat{h}}_{l}}{{{\overset{\sim}{h}}_{i}}{{\overset{\sim}{h}}_{l}}} \right)}} & (6)\end{matrix}$where i and l denote the packet indices whose corresponding channelvectors are compared. Other candidates for a test statistic includeEuclidean distance between the channels, as described by D. B. Faria andD. R. Cheriton, “Detecting identity-based attacks in wireless networksusing signal prints,” in WiSe '06: Proceedings of the 5th ACM workshopon Wireless security. New York, N.Y., USA: ACM, 2006, pp. 43-52; N.Patwari and S. K. Kasera, “Robust location distinction using temporallink signatures,” in MobiCom '07: Proceedings of the 13th annual ACMinternational conference on Mobile computing and networking. New York,N.Y., USA: ACM, 2007, pp. 111-122; L. Xiao, L. Greenstein, N. Mandayam,and W. Trappe, “Fingerprints in the ether: Using the physical layer forwireless authentication,” in Communications, 2007. ICC '07. IEEEInternational Conference on, June 2007, pp. 4646-4651; and“Channel-based spoofing detection in frequency-selective Rayleighchannels,” Wireless Communications, IEEE Transactions on, vol. 8, no.12, pp. 5948-5956, 2009, and difference in total channel power. However,the angle based statistic has two properties that make it attractive fora reconfigurable antenna based authentication scheme. Depending on theenvironmental conditions, channels from certain modes may be strongerthan the others. Such stronger channels tend to dominate the value ofthe computed test statistic in distance or power based metrics,rendering the information contained in the weaker channels useless.However, the angle based test statistic weights channels from all themodes equally, resulting in better utilization of all the availableinformation. The support of the test statistic is naturally limited(0°≤θ≤360°) and hence smoother distribution functions can be formed witha limited number of training samples. This same property will also bedesirable when offline learning techniques based on standard wirelesschannel models are employed to train the system.

Since the test statistic is the angle between the two spatialsignatures, the vectors can be normalized without altering its value.Therefore, θ can now be written as:

$\begin{matrix}{\theta = {\cos^{- 1}\left( {{\hat{h}}_{i} \cdot {\hat{h}}_{l}} \right)}} & (7) \\{= {\cos^{- 1}\left( {\sum\limits_{n = 1}^{N}{{{\overset{\_}{h}}_{ni}}{{\overset{\_}{h}}_{nl}}}} \right)}} & (8)\end{matrix}$where

${\overset{\_}{h}}_{i} = {\frac{{\hat{h}}_{i}}{{\hat{h}}_{i}}\mspace{14mu}{and}\mspace{14mu}{\overset{\_}{h}}_{ni}}$denotes the elements of the normalized vector. Moreover, a bar denotesthe modified quantity after normalization in the proceeding discussion.

The duration of shadowing is long compared to the packet transmissiontimes and considered to be constant for all antenna configurations atany channel estimation period. Therefore, at time instant i, the channelcorresponding to a terminal is given by:

$\begin{matrix}{{\overset{\_}{h}}_{i} = \begin{bmatrix}{{{{{\overset{\_}{X}}_{i}{\overset{\_}{h}}_{i\; 1}} +}{\overset{\_}{\epsilon}}_{i\; 1}{+ {\overset{\_}{n}}_{i\; 1}}}} \\{{{{\overset{\_}{X}}_{i}{\overset{\_}{h}}_{i\; 2}} + {\overset{\_}{\epsilon}}_{i\; 2} + {\overset{\_}{n}}_{i\; 2}}} \\\vdots \\{{{{\overset{\_}{X}}_{i}{\overset{\_}{h}}_{i\; N}} + {\overset{\_}{\epsilon}}_{i\; N} + {\overset{\_}{n}}_{iN}}}\end{bmatrix}} & (9)\end{matrix}$From equations (9) and (8), the angle between this vector and anotherspatial signature at time instant l is given by:

$\begin{matrix}{\theta = {\cos^{- 1}\left( {\sum\limits_{n = 1}^{N}{{{{{\overset{\_}{X}}_{i}{\overset{\_}{h}}_{i\; n}} + {\overset{\_}{\epsilon}}_{i\; n} + {\overset{\_}{n}}_{i\; n}}}{{{{\overset{\_}{X}}_{i}{\overset{\_}{h}}_{i\; n}} + {\overset{\_}{\epsilon}}_{i\; n} + {n_{i\; n}\bullet}}}}} \right)}} & (10)\end{matrix}$where X _(i) h _(in)+∈ _(in)+n _(in) involves the sum of a log normalrandom variable and a normal random variable for which a tractableclosed form pdf expression does not exist. Therefore, empirical densityfunctions for θ obtained from measurements will be used in the analysis.

Previous studies (e.g. Medbo) have shown that the variable component ∈is usually between 20 and 50 dB lower than the static component for amajority of the time. Therefore, for a simpler case where |∈+n|<<|Xh|,ĥ_(n) can be written as:ĥ _(n) ≈Xh _(n)  (11)andh _(i) =X _(i) [|h _(i1) ||h _(i2) | . . . |h _(iN)|]  (12)Normalizing h_(i) removes the effect of X_(i) and can be written as:

$\begin{matrix}{{h^{-}{\,_{\downarrow}i}} = \begin{bmatrix}{{h^{-}{\,_{\downarrow}i}\; 1}} & {{h^{-}{\,_{\downarrow}i}\; 2}} & \ldots & {{h^{-}{\,_{\downarrow}i}\; N}}\end{bmatrix}} & (13) \\{and} & \; \\{\theta = {\cos^{- 1}\left( {\sum\limits_{n = 1}^{N}{{{\overset{\_}{h}\,_{i\; n}}}{{{\overset{\_}{h}}_{i\; n}\bullet}}}} \right)}} & (14)\end{matrix}$which is the ‘true’ angle between the two channels corresponding to thetwo locations from which packets i and l originated.

Given the authentication metric θ, the problem of classifying thetransmitter now becomes a hypothesis testing problem. The nullhypothesis H_(D) is picked to be that the incoming packet is from thesame legitimate transmitter T and the alternate hypothesis H_(i) to beotherwise. Denoting the transmitter corresponding to h_(i) as T(h_(i)),the test can be written as:H _(D) :T(h _(i))=T(h _(i))  (15)H ₁ :T(h _(i))≠T(h _(i))  (16)The conditional probability distributions of the authentication metric θand the corresponding cumulative distribution functions may be denotedas follows:H _(↓)0:p _(↓)θ(d|H _(↓)0),(_(↓)0(θ)  (17)H _(↓)1:p _(↓)θ(d|H _(↓)1),(_(↓)1(θ)  (18)For a given false alarm rate α, a threshold λ can be found such that:

$\begin{matrix}{\alpha = {{p_{\theta}\left( {{\theta > \lambda}❘H_{0}} \right)}(19)}} \\{= {1 - \left( {{\,_{\downarrow}0}(\lambda)\mspace{495mu}(20)} \right.}} \\{\left. \Rightarrow\lambda \right. = \left( {{{}_{}^{}{}_{}^{}}\left( {- 1} \right)\left( {1 - \alpha} \right)\mspace{430mu}(21)} \right.}\end{matrix}$The probability of missed detection β can be defined for this thresholdas:β=p(θ<λ|H ₁)=(_(↓)1

(*(*

_(↓)0^(↑)(−1)(1−α))  (22)For a given authentication metric θ, estimates for α and β may now beformed.Measurement Setup and Reconfigurable Antenna

Channel measurements to evaluate the performance of the reconfigurableantenna based user identification scheme of the invention were performedusing a four port vector network analyzer (VNA) (Agilent N5230A) bymeasuring S₂₁ between the transmitter and receivers. The location chosenfor the measurements was a medium sized laboratory on Drexel Universitycampus. The laboratory is 20 m long, 8 m wide, and 4 m high. The lab hasa back room separated from the main lab by a plaster wall and severalcubicles segmented by metallic walls and has other typical laboratoryfurniture, electronic equipment, and cabling scattered throughout theroom. The measurement layout and setup is shown in FIG. 3. Transmitter Tand intruder I locations were chosen so that there were a combination ofboth line-of-sight (LOS) and non-line-of-sight (NLOS) links. Receiver Rwas equipped with the reconfigurable antenna to be described below. Tand I were equipped with omnidirectional whip antennas. The antenna atthe receiver was mounted at a height of 2.5 m while the antennas at thetransmitters were mounted at the desk level of approximately 0.75 m.

The frequency was swept over a 22 MHz bandwidth centered at 2.484 GHzwhich corresponds to channel 14 of the IEEE 802.11n standard. 64 evenlyspaced frequency samples were measured over this bandwidth. Twolocations for R and four locations for T were chosen yielding a total ofeight links. For each of these links, ten different I locations wereconsidered. For each (R,T,I) pair, channels corresponding to the T-R andI-R links were measured for 5 different antenna configurations at Revery 10 seconds for a total of 1000 samples. The time to complete eachsweep was automatically set by the VNA to 130 msec. Due to speedlimitations in the control board for changing antenna modes, a 0.25second delay was introduced while switching between different antennamodes. Measurements were taken over several days during both morning andevening hours when the human traffic was moderate and low, respectively.

The reconfigurable antenna used in the experimental setup is a two-portmicrostrip composite right/left-hand (CRLH) transmission line leaky waveantenna (LWA) which is an antenna design inspired by meta-materialtransmission lines. See, e.g., D. Piazza, M. D'Amico, and K. Dandekar,“Performance improvement of a wideband MIMO system by using two-portRLWA,” Antennas and Wireless Propagation Letters, IEEE, vol. 8, pp.830-834, 2009. Pattern reconfiguration in this antenna is achieved byvarying the right and left handed capacitances of a leaky CRLHtransmission line by means of varactor diodes placed on the structure.The phase constant of the unit cells that constitute the antenna ischanged by varying the bias voltage on the varactor diodes which resultsin beams directed in different directions for a fixed frequency ofoperation. The patterns in the elevation plane for the five modes usedin this study are shown in FIG. 4. The choice of this antenna isjustified by its ability to electrically steer the antenna beam whilehaving a significantly compact form factor.

Channel Correlation

The N elements of the decision vector ĥ correspond to channels estimatesfor the different antenna modes used in the reconfigurable antenna(i.e., this scheme is based on exploiting pattern diversity). However, asimilar scheme could be devised by utilizing channel coefficientscorresponding to N different frequencies (frequency diversity), orspatial snapshots (spatial diversity). The amount of correlation thatexists between the elements in ĥ for different diversity schemes willnow be empirically quantified.

The pattern correlation coefficient between radiation patternscorresponding to antenna modes i and j is defined as:ρ_(↓)(i,j)=(∫_(↓)4π

E

_(↓) j(Ω)E _(↓) i ^(↑)|(Ω)dΩ)/√(∫_(↓)4π*(*E _(↓) i(Ω)(^(↑)2dΩ

∫

_(↓)4π*(*E _(↓) j(Ω)(^(↑)2dΩ)  (23)where E_(i)(Ω) is the radiation pattern for the ith mode and † denotescomplex conjugation. The correlation coefficients generated by thisdefinition between azimuthal patterns for five different modes arelisted in Table I.

TABLE I Pattern correlation coefficients between different modes of theLWA Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 1 1 0.73 0.42 0.10 0.06 Mode2 0.73 1 0.82 0.27 0.07 Mode 3 0.42 0.82 1 0.55 0.11 Mode 4 0.10 0.270.55 1 0.56 Mode 5 0.06 0.07 0.11 0.56 1

Channel correlation coefficients with respect to the first antenna mode,averaged over the eight T-R links, are shown in FIG. 5. The first row ofTable I is superimposed on FIG. 5 to illustrate the influence of patterncorrelation on the resulting channel correlations. FIG. 5 follows theconventional wisdom that uncorrelated patterns lead to uncorrelatedchannels in rich multipath environments. The channel correlationcoefficients with respect to the first measured frequency for the otherfrequencies are also shown in FIG. 5. This result agrees with well-knownpublished results as well. However, of interest to the inventors is thecomparison between the correlations arising from pattern and frequencycorrelations.

In the measured environment, approximately a 5 MHz frequency separationwas required to achieve a correlation factor of 0.2 and 11 MHzseparation for 0.1. However, relying on frequency separation for channeldecorrelation presents two problems. The first problem is that it is notstraightforward to estimate the frequency separation required for agiven level of decorrelation without proper knowledge of the RMS delayspread of the environment. Second, most wireless systems are bandlimited and the ability to span the frequency axis to achieve a requiredlevel of decorrelation may not be possible for many applications. On theother hand, using pattern diversity for applications requiringdecorrelated channel realizations is a more ‘controlled’ approach whereantenna modes can be designed to exhibit a certain level ofdecorrelation which will translate to a similar level of decorrelationin the realized channels. For example, with just two modes (mode 1 and5), the inventors are able to achieve correlation levels of less than0.05. These correlation trends will serve to gain insights on some ofthe results to be discussed below.

Numerical Results

The measurements gathered as described above were analyzed to quantifythe performance of the reconfigurable antennas based authenticationscheme of the invention. For a given N, α and β were obtained asfollows:

1) Pick a (R, T, I) combination and a frequency.

2) Pick N adjacent antenna modes (e.g., for N=3 possible selections are(1,2,3), (2,3,4), and (3,4,5)). ĥ's used in the following steps areformed by stacking the channels corresponding to the modes present inthis combination.

3) Compute p_(θ)(θ|H₀) by gathering θ's corresponding to T-R's ĥ at timeinstants i and i+1(1≤i≤999).

4) For different α determine the corresponding λ from this distribution.

5) Compute p_(θ)(θ|H₁) by gathering θ corresponding to T-R ĥ at timeinstant i−1 and I-R ĥ at time instant i (2≤i≤1000).

6) From the different λ computed in step (3), determine thecorresponding miss rate β.

7) Repeat steps (3-6) for all possible mode combinations.

8) Repeat steps (2-7) for all possible (R, T, I) combinations.

9) β is averaged over all the possible combinations repeated in steps(7) and (8).

Similarly, for frequency diversity, different antenna modes instead offrequencies are picked in step (1) and N adjacent frequencies are choseninstead of antenna modes in step (2).

FIG. 6 shows the ROCs obtained for three different mode pairs (out often possible pairs) when two modes are used for authentication. Theworst performing mode corresponds to the mode pair of (2,3). This paircan be seen to have the highest pattern correlation from Table I. Thebest performing mode corresponds to the mode pair (1,4) which is nearthe lowest correlation level observed among the radiation patterns.Similar trends can be observed when frequency diversity is employed aswell. However, large frequency separations (more decorrelation) arerequired between the frequency points used to obtain good performance.

The reason for the detection rate dependence on the correlation betweenthe elements in ĥ can be explained as follows. Assume two modes orfrequencies are highly correlated. Due to environmental conditions or bydeliberate manipulation (such as transmit power control, trying outdifferent locations, etc.), the intruder's channel corresponding to onemode may fall close to that of the legitimate transmitter. Now theprobability of the other mode to fall close to that of the transmitteris also increased due to the high correlation and thus the addition ofthe new mode does not increase the quality of the spatial signaturecontained in ĥ. However, if the modes are decorrelated, the ability foranother user to accidentally or intentionally match all the channels ofanother user becomes probabilistically more difficult. Thus, moredecorrelated elements in the decision vector ĥ lead to improvement indetection rates. It is therefore clear that higher levels of patterncorrelation impede performance and hence the different antenna modesused in the scheme should have low decorrelation between them.

FIG. 7 shows the performance of the pattern diversity based scheme indetecting intruders for different values of N. For an α of 1%, βdecreases from 30% to 3% when N is increased from 2 to 5. For a given α,β decreases with N. As N grows higher, the probability for the intruderchannel to closely match all the channel elements in ĥ such that θ fallsbelow threshold λ and becomes low and hence the detection rate improves.

It can be observed that the improvement in performance starts to reduceas N is increased. For example, for an α of 1%, β improves by 15% when Ngoes from 2 to 3. This improvement reduces to 2% when N increases from 4to 5. Introducing an additional mode into ĥ does not necessarily keepthe average inter-element correlation at the same level before itsintroduction due to the different levels of correlation that existsbetween different modes. Due to the limited number of modes used in thestudy, this is especially true for higher N (≥4) since ĥ consists ofhighly correlated modes and their contribution to the detection rate isonly minimal. Hence, it can be observed that there are diminishingreturns in performance improvement as the number of modes increases. Todemonstrate this effect, frequency diversity is used where the multipleelements in ĥ are picked to have low correlation between each other andthe average correlation does not change when a new element isintroduced. Frequencies are picked that are separated by 5 MHz(resulting channel correlation <0.2 from FIG. 5) for different values ofN.

FIG. 8 shows the resulting ROCs which indicates that as long as theaverage correlation among the elements is not diminished, introducingnew modes or frequencies in ĥ will maintain the rate of improvement indetection rates. However, this phenomena should not discourage the useof a reconfigurable antenna based solution since a multitude ofreconfigurable antenna geometries exist that can generate several modeswith very low correlation amongst all their patterns. See, e.g., D.Piazza, P. Mookiah, M. D'Amico, and K. Dandekar, “Experimental analysisof pattern and polarization reconfigurable circular patch antennas forMIMO systems,” Vehicular Technology, IEEE Transactions on, vol. 59, no.5, pp. 2352-2362, June 2010.

Finally, the performance of this scheme when operating in an online modewas analyzed. The number of samples from T used for initially estimatingp_(θ)(θ|H₀) is denoted by N_(T-θ) corresponding to all the N_(T) ^((N)^(T) ⁻¹⁾/2 samples used for forming this distribution from which λ wascomputed for different α. The most recent channel estimate to pass theauthentication process was held in memory for the next test. FIG. 9shows the realized α during this online operation for two differentvalues of N_(T). It can be observed that more training leads to goodperformance. ROCs with respect to the achieved α is shown in FIG. 10.The observed trends are comparable to that of the loose upper bound forperformance obtained from the offline mode of analysis shown in FIG. 7.

A key issue relates to how the channel estimates can be obtained for allthe different modes without degrading throughput and power consumption.FIG. 11 shows a possible structure of a transmit frame for use with thissecurity scheme. The antennas can cycle through the modes during thetransmission of an extended packet during which the channel estimationis also performed for the different modes. Padding is inserted betweenthe payload and next training sequence to leave sufficient time for theantenna to change modes. Switches with speeds on the order ofpicoseconds do exist currently and can lead to shorter pad lengthsrequired while switching between modes.

Thus, a reconfigurable antenna based physical layer authenticationscheme is provided in accordance with a first embodiment of theinvention by taking channel measurements on a VNA and combining channelinformation from different antenna configurations. The resultingconfiguration has been shown to result in improved intruder detection.The relationship between the correlation among the elements in thedecision metric and the authentication performance shows that theachieved performance improves as the average decorrelation that existsbetween the different antenna modes decreases. By choosing modes thatare highly decorrelated, high performance levels can be obtained evenwhen operating in a system with very limited bandwidth. The performanceof the scheme improves with more training in terms of detection rates aswell as with realized false alarm rates approaching designed falsealarms rates. Therefore, next generation wireless systems that will beequipped with reconfigurable antennas can benefit from this scheme byemploying the antennas to add an additional layer of security at thephysical layer.

Intrusion Detection Scheme for Wireless Networks

Problem Definition and Threat Model

The problem that is addressed by the second exemplary embodiment of theinvention is one of detecting an intruder who has gained access into thesystem by means of hijacking a connection already established by alegitimate user. The problem scenario again consists of three players:the receiver R, transmitter T and intruder I. Transmitter T and receiverR have established a connection and are in the process of exchanginginformation as shown at the top of FIG. 12. Intruder I eavesdrops intothis connection and waits until he gathers sufficient information tospoof T. A surprisingly large number of vulnerabilities exist in modernwireless access technologies that allows I to obtain this informationwith relative ease. Once this information is obtained, I launches aspoofing attack by posing as T to R as shown at the bottom of FIG. 12.

To gain a practical perspective of the problem, R can be thought of as awireless access point through which T is connected to the organizationalnetwork. I can be an adversarial entity whose objective is to gain entryinto the organizational network, hijack T's connection with R or launcha man-in-the-middle attack on the connection between T and R, amongother possibilities. The objective of the security scheme is to detectthis change in the real transmitter at R in order to initiate countermeasures.

To achieve his goal, I can be equipped with a powerful transceivercapable of passively monitoring and capturing all traffic between T andR and sufficient computational resources to analyze the traffic toexploit the vulnerabilities in relatively quick time. I can be anexternal adversary attempting to launch an attack on the network fromoutside the organization's premises or an internal entity who isinterested in launching an attack on T. In both cases, it is noted thatI cannot be physically co-located with T, which forms the basis of themethod for intrusion detection in accordance with an exemplaryembodiment of the invention.

It should be noted that I's motive is to compromise T's identity in thenetwork and therefore it is imperative for I that T first initiates andestablishes a connection with R. Therefore, it is assumed that I willnot resort to jamming attacks to prevent T from establishing asuccessful connection with R.

Additionally, it is assumed that only R is equipped with areconfigurable antenna with M modes since it is more likely that anaccess point is equipped with such an antenna than a user terminal dueto cost and space constraints. Therefore, it is also assumed that T andR are equipped with standard omni-directional antennas.

As stated earlier, the proposed solution exploits the fact that T and Ihave to be located in two different physical locations which would bemanifested by two different channel distributions sensed by R. Due tothe multipath structure of the environment, I cannot methodicallymanipulate the channel between itself and R in such a way as to imitatethe channel between T and R. This is because it does not and cannot knowthe channel between T and R. Introducing reconfigurable antennas to thesolution adds multiple channel distributions corresponding to each modeused in the antenna. This makes the problem of closely matching thechannel corresponding to T even more challenging for I which results inenhanced protection. However, it should be noted that the scheme of theinvention does not attempt to localize T or I. Instead channelinformation pertaining to the different antenna modes is used to detectI if it compromises the existing link between T and R.

Description of Intrusion Detection Scheme

With the notable exception of mobile networks, many current and emergingwireless data networks are associated with stationary terminals at bothends of the link. Temporal variations in channels related to suchnetworks arise mainly due to movements of people and objects in thevicinity of the terminals as well as small localized movement of theterminals within a very small area. See, e.g., J. Medbo, J.-E. Berg, andF. Harrysson, “Temporal radio channel variations with stationaryterminal,” Vehicular Technology Conference, 2004. VTC2004-Fall. 2004IEEE 60th, pages 91-95, Vol. 1, 2004; C. Oestges, D.Vanhoenacker-Janvier, and B. Clerckx, “Channel Characterization ofIndoor Wireless Personal Area Networks,” Antennas and Propagation, IEEETransactions on, 54(11):3143-3150, 2006; and P. Pagani, and P. Pajusco,“Characterization and Modeling of Temporal Variations on anUltrawideband Radio Link,” Antennas and Propagation, IEEE Transactionson, 54(11):3198-3206, 2006. A typical example for such a scenario wouldbe a user seated at a bench in a public place accessing the network froma laptop connected to an access point in the vicinity. The secondembodiment of the invention addresses intrusion problems that pertain tosuch wireless network usage scenarios and does not address large scaleterminal mobility.

The amplitude of the estimated complex channel coefficient correspondingto a single frequency carrier g, is denoted by h. The probabilitydistribution of h follows a Ricean or Rayleigh distribution. The latterdistribution with parameter σ is chosen to describe h for reasons thatwill be discussed below:

$\begin{matrix}{{p_{\sigma}(h)} = {\frac{h}{\sigma_{2}}e^{{{- h^{2}}/2}\;\sigma^{2}}}} & (24)\end{matrix}$

During the connection establishment process, σ=σ₀ corresponding to T isestimated through a sequence of training packets. At some time instantwhen I succeeds in spoofing T, it will hijack this connection. However,since I is at a physically different location, σ=σ₁ corresponding tothis link will be different from σ₀ and will be unknown.

Let h_(i) (i∈Z,i>0) be a sequence of observed i.i.d. channel estimatesfrom the incoming packets after the initial training stage and h=[h_(j),. . . , h_(k)]. i can be taken to denote the packet or time index.N=k−j+1 is the block size. If σ(h) is denoted as the σ value of theRayleigh distribution from which the elements of h originated, theintrusion detection problem can be now formulated as a hypothesistesting problem as follows:H ₀:σ(h)=σ₀  (25)H ₁:σ(h)≠σ₀  (26)

The invention employs a Neyman-Pearson detector which decides H₁ if thelikelihood ratio exceeds a threshold:

$\begin{matrix}{{L(h)} = {{\log\left( \frac{p_{\sigma_{1}}\left( {h;H_{1}} \right)}{p_{\sigma_{0}}\left( {h;H_{0}} \right)} \right)} > \gamma}} & (27)\end{matrix}$However σ₁ is not known in this case. In this case, it is well knownthat the GLR test which replaces σ₁ with its MLE estimate isasymptotically the uniformly most powerful among all tests. Hence, theGLR test that uses the MLE of σ₁ denoted by {circumflex over (σ)}₁.Estimation is done over the elements in block h. The MLE for σ₁ ² isgiven by:

$\begin{matrix}{{\hat{\sigma}}_{1}^{2} = {\frac{1}{2N}{\sum\limits_{i = j}^{k}h_{i}^{2}}}} & (28)\end{matrix}$Substituting (28) in (27) and simplifying yields:

$\begin{matrix}{{L(h)} = {\left( \frac{2N\;\sigma_{0}^{2}}{\lambda} \right)^{N}e^{({\frac{\lambda}{2\;\sigma_{0}^{2}} - N})}}} & (29)\end{matrix}$where λ=Σ_(i=j) ^(k)h_(i) ².

The use of multiple antenna modes will result in M different channelrealizations at each time instant. The environment ‘seen’ by thedifferent modes of the antennas will be different due to the differencesin their radiation patterns and therefore the distribution for each ofthese M channel realizations will be characterized by different σ's.Assuming that the channel realizations yielded by the different antennamodes are independent, then:

$\begin{matrix}{{L(h)} = {{\log\left( {\sum\limits_{m = 1}^{M}\frac{p_{\sigma_{1\; m}}\left( {h_{m};H_{1}} \right)}{p_{\sigma_{0\; m}}\left( {h_{m};H_{0}} \right)}} \right)} > \gamma}} & (30)\end{matrix}$where σ_(0m) and σ_(1m) are the distributions' parameters for mode munder the null and alternate hypothesis respectively. h_(m) representsthe channel vector for mode m. The decision function simplifies to:

$\begin{matrix}{{L(h)} = {\sum\limits_{m = 1}^{M}\left\lbrack {\left( \frac{2N\;\sigma_{0\; m}^{2}}{\lambda_{m}} \right)^{N}e^{({\frac{\lambda}{2\;\sigma_{0m}^{2}} - N})}} \right\rbrack}} & (31)\end{matrix}$where λ_(m)=Σ_(i=j) ^(k)h_(im) ² and h_(im) denotes the channelrealization at time instant i for the m^(th) antenna mode. The controlparameters that can be used to tune the performance of this scheme arelisted in Table II.

TABLE II Control Parameters Parameter Description N Block size. Numberof most recent consecutive channel estimates used in the test includingthe estimate corresponding to the packet under test. N_(T) Number oftraining packets used to estimate σ₀ during connection initialization γThreshold. Can be set based on the values of L(h) observed during thetraining phase. N_(D) Detection delay. Maximum number of packets from Iwithin which it should be detected. If detection doesn't happen by thistime, it is considered a missed detection. N_(F) Number of packets fromT before I takes over. Though this is not a controllable parameter inreal time, it has a critical effect on the false alarm rate. M Number ofantenna modes.

A graphical depiction of these parameters is shown with respect to asample evolution of L(h) in FIG. 13.

Detection Scheme

Steps of the detection scheme in an exemplary embodiment include:

1. During the outset of the session, R estimates σ₀ through a trainingsequence. The number of packets used for training is denoted by N_(T).

2. R also computes L(h) for j=i−N+1 and k=i based on these channelestimates at each instant i (N≤i≤N_(T)).

3. Actual transmissions begin from T and R continues to compute L(h) foreach packet transmission. I is assumed to hijack this connection andstarts transmitting to R after N_(F) transmissions from T.

4. Based on these computed L(h) during the training phase, a threshold γis picked such that an alarm is raised whenever L(h)>γ.

5. In the event of an alarm, a higher layer re-authentication procedurecan be evoked to reverify the identity of the transmitter.

Threshold Selection:

The value of γ will be chosen based on the values observed for L(h)during the training period. If the maximum value of L(h) observed duringtraining is L_(M)(h), γ can be expressed as KL_(M)(h) where K is thescaling factor that needs to be controlled in order to achieve thedesired detection and false alarm rates. In accordance with thisembodiment of the invention, selection of K is performed in an adaptivemanner. One starts with K=1 and gradually increases it's value until anacceptable false alarm rate is achieved.

The connection can be vulnerable to an attack during this thresholdselection phase as well. Therefore, higher layer authenticationprotocols (e.g. 802.11i) should be evoked to verify false alarms duringthis adaptation process to ensure security until the target value of Kis reached though this may cause some processing overhead due tofrequent re-authentication. Optionally, depending on the level of threatto which the network is exposed to, this re-authentication process canbe relaxed during this adaptive threshold determination phase for moreefficient operation and all alarms may be treated as false alarms.

Channel Measurements

Channel measurements were performed on Drexel University campus using afour port vector network analyzer. The measurement environment and nodelocations are the same as described above with respect to FIG. 3. As inthe first embodiment, the measurements were performed with R equippedwith a reconfigurable leaky wave antenna of the type disclosed by D.Piazza, M. D'Amico, and K. R. Dandekar, “Performance Improvement of aWideband MIMO System by Using Two-Port RLWA,” Antennas and WirelessPropagation Letters, IEEE, 8:830-834, 2009. The radiation patternscorresponding to the five modes used in the study are shown in FIG. 14.T and I were equipped with standard monopoles. Measurements wereperformed at 2.484 GHz which corresponds to the center frequency ofchannel 14 of the 802.11 band. Two R, four T and ten I locations werechosen which yielded a total of eight R-T links each with thencorresponding R-I links. For each (R, T, I) combination, 1000 timesnapshots were recorded for the R-T and R-I links for the 5 differentantenna modes. Measurements were performed during different hours of theday over several days during which there was low to moderate movement inthe environment.

Why Rayleigh Distribution?

It has been assumed that the channel amplitudes follow a Rayleighdistribution instead of the more general Ricean distribution. In orderto justify this assumption, the empirical distribution functionsobtained for each link from the measured data was compared to a Rayleighor Ricean distribution whose parameters were estimated from themeasurements. The similarity between the empirical distribution (p_(e))and standard distribution (p_(p)) for each link is quantified throughtwo metrics: the total variation distance between the distributions andthe Kullback-Leibler (KL) divergence.

The total support S is defined as:min(S _(e) ,S _(p))≤S≤max(S _(e) ,S _(p))  (32)where S_(e) and S_(p) are the supports of the empirical and standarddistributions respectively. S is discretized into T evenly spaceddiscrete points. The total variation distance between the twodistributions is defined as:

$\begin{matrix}{e = {\frac{1}{2}{\sum\limits_{t = 1}^{T}{{{p_{e}\left( h_{t} \right)} - {p_{p\;}\left( h_{t} \right)}}}}}} & (33)\end{matrix}$where p_(e)(h_(t)) and p_(p)(h_(t)) denote the values of thedistributions evaluated at the t^(th) discrete point in S. The KLdivergence between p_(e) and p_(p) is defined as:

$\begin{matrix}{{D_{KL}\left( {p_{e}{Pp}_{p}} \right)} = {\sum\limits_{t = 1}^{T}{{p_{e}\left( h_{t} \right)}\log_{2}\frac{p_{e}\left( h_{t} \right)}{p_{p}\left( h_{t} \right)}}}} & (34)\end{matrix}$

Table III lists the trends in the observed values over all the measuredlinks for the difference between the empirical distribution and the twostandard distributions.

TABLE III Difference between Empirical and Parametric DistributionsStandard Mean KL Distribution Mean of e Deviation of e DivergenceRayleigh 0.059 0.014 1.56 Ricean 0.036 0.014 0.32As can be observed, though the channel distributions are not ‘purely’Rayleigh or Ricean, which is to be expected, they resemble thesedistributions sufficiently enough to provide the inventors with theability to develop an analytical framework for the problem. Moreover, asthe values indicate, on average, due to the combination of line-of-sight(LOS) and non-line-of-sight (NLOS) of links, modeling the channel asRayleigh does not lead to a large error compared to modeling it asRicean in the system, though the observed distributions marginallyresemble the Ricean distribution more than the Rayleigh. Nevertheless,Rayleigh distribution was picked over Ricean for three reasons. Closedform MLE estimates do not exist for the parameters that characterizeRicean distributions and it requires recursive methods that arecomputationally intense. See, e.g., J. Sijbers, A. J. den Dekker, P.Scheunders, and D. Van Dyck, “Maximum-likelihood estimation of Riciandistribution parameters,” Medical Imaging, IEEE Transactions on,17(3):357-361, 1998. The second reason is that when small values of Nare used in the scheme, the recursive scheme does not achieveconvergence resulting in very poor estimates that will have asignificantly negative effect on the scheme's performance. Finally, asimpler form of GLRT function cannot be formulated due to the Besselfunctions that characterize Ricean distributions which will lead tohigher computational complexity. Based on these observations andreasons, the channel was modeled as Rayleigh distributed.Analysis and Results

The performance of the intrusion detection scheme was studied in termsof the probability of missed detection (β) and false alarm rates (α) asa function of the different control parameters listed above. α and βcharacteristics presented in this section were computed from themeasured channels as follows:

1. For each (R, T, I) combination, a detection threshold γ was obtainedthrough the first N_(T) training samples.

2. For the N_(F) subsequent samples from T, the number of instanceswhere L(h) exceeds γ was recorded. A false alarm was recorded when thenumber of instances was greater than one.

3. The friendly samples were followed by samples from I. A detection wasrecorded if L(h) exceeds γ within the first N_(I) transmissions from I.If not, a miss was recorded.

4. This process was repeated for 100 trials with different subsets offriendly and adversary samples and the average α and β were computed.

5. The overall α and β were computed as the average obtained over allpossible (R, T, I) combinations.

Unless specifically stated otherwise, the presented results also reflectthe average over the different antenna combinations possible for a givenM, i.e., for a given α, the presented missed detection probabilities areaverages obtained over the (⁵ _(M)) possible combinations for a given M.

Single Antenna Mode (M=1)

FIG. 15 shows the average detection error tradeoff (DET) curves for asingle antenna mode for different values of block size N. The nonlinearscaling of the axes in a DET curve is designed to yield a straight linewhen L(h) from the system follows a normal distribution. The diagonalline defined by β=−α represents completely random performance and curvesthat lie on the quadrant left of this line represent positive levels ofperformance.

It can be observed that the performance improves with block size. Thisis due to two reasons. A larger block size gives a better estimate fora, and hence when the intruder starts injecting packets, the differencebetween σ₀ and σ₁ becomes more clear which in turn results in L(h)growing above the threshold rapidly. Moreover when N is large, theincreased contribution from channels corresponding to I in L(h) afterthe intrusion will result in a rapid increase in its value as well.

Moreover, the values of N used in the computation of L(h) are notsufficiently large enough to yield a Gaussian behavior and therefore theDET curves do not exhibit a linear trend. While such a Gaussian behavioris preferred since it allows us to resort to standard normaldistributions to set the threshold γ, it will not be possible to employa sufficiently large N to yield this behavior since a meaningful minimumdetection delay N_(D) is determined by the block size.

However, with just a single antenna mode, the achievable detection ratesare unacceptably low at low α regions. In cases where σ₁ and σ₀ are notwell separated, the level of increase in L(h) after intrusion will notbe sufficient enough to match the γ that is required to maintain a lowα, which in turn leads to poor detection rates. To gain insights intothis, the maximum percentage difference between σ's among the differentantenna modes is defined as:

$\begin{matrix}{P = {\max\limits_{{m = 1},\;\ldots\;,\; M}{\frac{{\sigma_{1m} - \sigma_{0m}}}{\sigma_{0m}} \times 100\%}}} & (35)\end{matrix}$

FIG. 16 shows the CDF of P for different values of M. Table IV listssome of the quantities extracted from these CDFs. When a single antennamode is employed, the mean maximum percentage difference is 75.5% andthe probability of this percentage difference being greater than 100% isas low as 0.07. This observation clearly elucidates the challenge withdesigning a GLRT based detection scheme using a single antenna. Thoughthe links can be differentiated in terms of σ, the amount of separationin σ₀ and σ₁ may not be sufficient in any given scenario for the GLRT toyield acceptable performance levels with a single antenna mode.

TABLE IV Statistics Pertaining to P from Measured Links M = 1 M = 2 M =3 M = 4 M = 5 Mean (P) 75.5 95.8 105.6 111.7 116.1 Median 76.2 86.6 88.990.4 91.5 Pr (P ≤ 100) 0.93 0.89 0.86 0.84 0.82

FIG. 17 shows the variation of probability of detection as a function ofdetection delay in terms of number of packets. Understandably, detectionrate improves with the allowable detection delay. However, it should benoted that timely detection of the intruder is very critical andtherefore N_(D) cannot be increased to arbitrarily large values toachieve the required detection rates. Again, it can also be observedthat the performance improves with block size. However, to be effective,higher values of N require that the detection delay to be at least aslong as the block size so that the block will contain samples entirelyfrom the intruder. The effect of N being less than the detection delaycan be observed by the dotted lines in FIG. 17 where the detectionperformance is significantly deteriorated.

The false alarm rate, as a function of the number of friendlytransmissions from T before I takes over is shown in FIG. 18. As onewould expect, the chances of raising a false alarm rises with morefriendly packets. A larger N results in a better estimate for σ₀ duringthe training phase. Additionally, it will yield a value for σ(h) that iscloser to the true σ₀ as well. Thus, the probability of L(h) to exceed γpicked based on the estimated σ₀ will be lower and hence α improves withN.

To summarize the preceding trends, higher N lowers α while improvingdetection rates. Though a longer detection delay can help detectionrates, in practice it is undesirable to have such long delays. However,due to the marginal difference between the σ values for the T-R and T-Ilinks, it is challenging to obtain acceptable detection rates whilekeeping the false alarm rates very low when using a single mode antennasystem. Hence, multi-mode antenna systems are used.

Multiple Antenna Modes

The multiple antenna mode case begins at FIG. 19, which shows the DETcurves achievable through the combination of channel informationcorresponding to multiple antenna modes. For each incoming packet, L(h)is computed as in (31) based on the channel information corresponding tothe chosen M configurations from which subsequent detection rates andfalse alarm rates are computed. It can be clearly seen that thedetection rate significantly improves with the number of modes for agiven α. Referring again to FIG. 16 and Table IV, it can be observedthat the maximum percentage difference between σ's among the differentantenna modes increases with M. This is by virtue of the fact thatdifferent antenna modes will exhibit different σ values and hence theprobability that the difference between σ₀ and σ₁ is very small for allthe modes will be lower. Thus, modes that exhibit a larger difference inσ will contribute more to the GLR test resulting in better performance.Increasing M increases the probability of finding modes that exhibit alarger difference in σ's and hence performance significantly improveswith M. Again due to the lower value of N, a non-Gaussian trend isobserved in the observed DET curves.

FIG. 20 shows the achievable detection rates as function of detectiondelay for the different M values. Comparing this with FIG. 17, it can beseen that the level of improvement achievable in detection rates isquite high with M as opposed to N. For example, by increasing N from 10to 25 results in a mere 5% improvement in detection when a single modeis used. Moreover, this improvement comes at the cost of a longerdetection delay. By introducing an additional mode, β can be loweredfrom around 20% to 9% while keeping N and N_(D) at 10.

FIG. 21 shows α as a function of the number of friendly packets. Asdescribed in step (2) above, α is defined as the probability that therewill be at least one packet that exceeds the threshold γ during thefriendly transmissions. Improvements in α is also observed withincreasing M. Naturally false alarms increase with increasing friendlypackets regardless of M. For relatively smaller values of N and a singleantenna mode, when certain samples in h come from the tail region of theunderlying Rayleigh distribution, the resulting estimate of {circumflexover (σ)}₁ can significantly diverge from σ₀ resulting in excursions ofL(h) above the threshold γ. However, when multiple antenna modes areemployed, the probability that the channels corresponding to most of themodes belong to the tail region at any given instant is reduced.Therefore at every time instant, the “well-behaved” modes help dampenthe hikes in {circumflex over (σ)}₁ due to the “stray” modes andtherefore help keep the excursions of {circumflex over (σ)}₁ above γ lowand hence reduce the probability of false alarm.

Which Modes to Choose?

From the above results is clear that introducing multiple antenna modesimproves the system's overall performance. However, these results do notprovide insights on how to pick the mode combinations and mostimportantly if there is any benefit in increasing the number of modesbeyond a certain level. Some insights to this problem can be found byanalyzing FIG. 22 and Table V. Table V lists the spatial patterncorrelation that exists between the radiation patterns corresponding tothe different antenna modes used in the study. The best, worst andaverage detection rates achieved by different individual modecombinations for M=2 and M=3 are shown in the figure. For M=2, it isevident that the detection rate is a function of the antenna correlationcoefficient. The best performance is achieved by the mode combination(5,1) which also has the lowest correlation between patterns. Thecombination with the highest correlation of 0.82 achieves the worstperformance. Similarly for M=3, detection rates exhibit the same trendwith respect to the average correlation between the different pair ofmodes within the combinations. Moreover, it can be seen that theperformance achieved by the best combination for M=3 outperforms the M=5case as well.

The above-described behavior can be attributed to the well knownphenomenon of decorrelated antenna patterns resulting in decorrelatedchannel realizations. The information provided by more decorrelatedchannel realizations serves to improve the ‘quality’ of L(h) and henceenables the scheme to distinguish between T and I more accurately.

Based on these trends, two guidelines are suggested for picking thedifferent antenna modes for minimizing intrusion. Antenna modes shouldbe picked such that the pattern correlation coefficient between thedifferent modes should be kept as low as possible. Many reconfigurableantenna architectures exist that can generate patterns with a very lowcorrelation coefficient between their modes. See e.g., J. Kountouriotis,D. Piazza, K. R. Dandekar, M. D'Amico, and C. Guardiani, “Performanceanalysis of a reconfigurable antenna system for MIMO communications,”Antennas and Propagation (EUCAP), Proceedings of the 5th EuropeanConference on, pages 543-547, 2011; and D. Piazza, P. Mookiah, M.D'Amico, and K. R. Dandekar, “Experimental Analysis of Pattern andPolarization Reconfigurable Circular Patch Antennas for MIMO Systems,”.Vehicular Technology, IEEE Transactions on, 59(5):2352-2362, 2010. Thesecond is that, adding new modes will improve detection rates as long asthe newly introduced mode does not diminish the average correlationcoefficient among the modes. This can be seen by observing the differentcircled pairs of DET curves in FIG. 22, where adding a new mode improvesdetection when the addition of the mode lowers the average correlationcoefficient among the modes.

TABLE V Pattern correlation coefficients between different modes of theLWA Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 1 1 0.73 0.42 0.10 0.06 Mode2 0.73 1 0.82 0.27 0.07 Mode 3 0.42 0.82 1 0.55 0.11 Mode 4 0.10 0.270.55 1 0.56 Mode 5 0.06 0.07 0.11 0.56 1Effect of Training

The quality of training will have a significant effect on theperformance of the scheme as the estimated σ₀ forms the basis for thelikelihood ratio based on which it operates. FIG. 23 shows the effect ofthe amount of training on the DET curves. As evidenced by the figure,longer training leads to better performance at the lower α regions asexpected. But interestingly, more training has a negative effect onsystem performance at the larger α regions. Recall that the threshold γis computed as KL_(M)(h) where L_(M)(h) is the maximum of L(h) observedduring training. Longer training on average leads to marginally largervalues for L_(M)(h). At high α regions, K≈1 and hence the threshold γ ismore sensitive to L_(M)(h). Therefore, for a given α, keeping all otherparameters constant while increasing only N_(T) results in an increasedestimate of the threshold γ, which in turn deteriorates detection.Although the estimate of σ₀ does improve with N_(T), the increase inL_(M)(h) overweights its benefit in the high α region leading toperformance degradation. Nevertheless, meaningful utilization of thisscheme will involve operating in the low false alarm region andtherefore longer training still will be preferred.

Practical Considerations

Some key practical issues need to be considered in order to make thisscheme work in practice. The most critical issue is the problem ofobtaining channel estimates over all the antenna modes on apacket-by-packet basis. FIG. 11 referenced above shows a possiblecandidate for a frame structure at the physical layer that can be usedto achieve this operation. As illustrated, an extended payload isinterspersed with the necessary training symbols for each mode alongwith padded intervals to allow for switching the antenna to a new modeand resynchronization. High speed switches with switching speeds in theorder of picoseconds currently exists that can allow the antenna toswitch modes at a rate compatible with current high data rateapplications.

As noted previously, the scheme of the second embodiment is proposed tocomplement existing higher level security protocols. Therefore, suchprotocols should continue to play their role in protecting the wirelesslink. An adaptive approach can be pursued when the GLR test triggers analarm at the physical layer. When an alarm is raised by the physicallayer scheme, the system can reconfigure the GLR test to operate in apoint on the DET curve that prioritizes low missed detection over falsealarms. Subsequent alarms should be handled by the the upper layerauthentication protocols such as 802.11i until it is ensured that theperceived threat does not exist after which point the GLR test canprioritize over false alarms again. Moreover, successfully adapting thealarm threshold will also rely on these re-authentication protocols.

Channel statistics may also gradually change with time which can lead toarbitrarily high false alarm rates. Periodic retraining can beimplemented to keep the system performance within acceptable levels.Therefore, this scheme can benefit from more comprehensive trainingalgorithms that continually update σ₀ based on packets that pass theintrusion detection test at the physical as well as upper layers.

The intrusion detection scheme of the second embodiment of the inventionutilizes physical layer information based on a reconfigurable antenna.The intrusion detection problem was setup as a generalized likelihoodratio test under the assumption of Rayleigh fading channels fordifferent antenna modes. The assumption was justified based on channelmeasurements gathered in an indoor environment using a network analyzer.The measurements were then used to study the performance of the schemeas a function of several control parameters available to the user. Itwas observed that large block sizes lower false alarm rates whileyielding high detection rates as well. By utilizing multiple modes in areconfigurable antenna concurrently in the likelihood function, it wasshown that the detection rates can be improved and false alarm rates canbe decreased while keeping the block size low. The pattern correlationcoefficient that exists between the radiation patterns of the differentantenna modes was shown to have a direct correlation with the resultingdetection performance, with lower pattern correlation resulting inbetter performance. In networks with very limited or non existentsecurity such as public WiFi spots, the proposed scheme can add an easyto implement layer of security that can provide improved levels ofprotection against intrusion. In more secure networks operating inhostile environments, this scheme in conjunction with existing higherlayer based security mechanisms can provide a much needed extra layer ofsecurity.

While the invention has been described with reference to specificembodiments, the description is illustrative of the invention and is notto be construed as limiting the invention. For example, those skilled inthe art will appreciate that the invention is typically implemented inpart as software that runs on a processor to perform the monitoring andprocessing functions described herein for measuring and processing thewireless channel information passing between the transmitter andreceiver. The present invention thus includes not only the disclosedmethods but also the programmed processor and associated computerreadable storage media containing such software as elements of thesystem for performing the methods described herein. Such features aswell as various modifications and applications may occur to thoseskilled in the art without departing from the spirit and scope of theinvention as defined by the appended claims.

Therefore, it must be understood that the illustrated embodiment hasbeen set forth only for the purposes of example and that it should notbe taken as limiting the invention as defined by the following claims.For example, notwithstanding the fact that the elements of a claim areset forth below in a certain combination, it must be expresslyunderstood that the invention includes other combinations of fewer,more, or different elements, which are disclosed above even when notinitially claimed in such combinations. For example, a practicalembodiment of the invention may include both the authentication schemeof the first embodiment and the intrusion detection scheme of the secondembodiment. A teaching that two elements are combined in a claimedcombination is further to be understood as also allowing for a claimedcombination in which the two elements are not combined with each other,but may be used alone or combined in other combinations. The excision ofany disclosed element of the invention is explicitly contemplated aswithin the scope of the invention.

The words used in this specification to describe the invention and itsvarious embodiments are to be understood not only in the sense of theircommonly defined meanings, but to include by special definition in thisspecification structure, material or acts beyond the scope of thecommonly defined meanings. Thus, if an element can be understood in thecontext of this specification as including more than one meaning, thenits use in a claim must be understood as being generic to all possiblemeanings supported by the specification and by the word itself.

The definitions of the words or elements of the following claims are,therefore, defined in this specification to include not only thecombination of elements which are literally set forth, but allequivalent structure, material or acts for performing substantially thesame function in substantially the same way to obtain substantially thesame result. In this sense, it is therefore contemplated that anequivalent substitution of two or more elements may be made for any oneof the elements in the claims below or that a single element may besubstituted for two or more elements in a claim. Although elements maybe described above as acting in certain combinations and even initiallyclaimed as such, it is to be expressly understood that one or moreelements from a claimed combination can in some cases be excised fromthe combination and that the claimed combination may be directed to asubcombination or variation of a subcombination.

Insubstantial changes from the claimed subject matter as viewed by aperson with ordinary skill in the art, now known or later devised, areexpressly contemplated as being equivalently within the scope of theclaims. Therefore, obvious substitutions now or later known to one withordinary skill in the art are defined to be within the scope of thedefined elements.

What is claimed:
 1. A method of detecting intrusion into a wirelesstransmission between a transmitter and a receiver in a communicationsystem using at least one multi-mode reconfigurable antenna, comprising:at a physical layer of the multi-mode reconfigurable antenna,determining wireless channel information between said transmitter andreceiver for different antenna modes of said at least one multi-modereconfigurable antenna; determining, based on the wireless channelinformation for the different antenna modes, a likelihood ratio functionassociated with the wireless channel information, wherein the likelihoodratio function comprises an estimate of cumulative wireless channelinformation between the transmitter and receiver; determining athreshold for the likelihood ratio function based at least on a maximumvalue generated by applying a generalized likelihood ratio test to asequence of channel estimate values generated during an initial trainingperiod of the transmitter; determining, via use of the generalizedlikelihood ratio test, if the likelihood ratio function exceeds thepredetermined threshold during the wireless transmission; and generatingan alarm when the predetermined threshold is exceeded, said exceedingbeing representative of an intrusion.
 2. The method of claim 1, whereinthe wireless channel information is provided for multiple decorrelatedmodes of the reconfigurable antenna.
 3. The method of claim 1, whereinthe predetermined threshold is a variable threshold.
 4. The method ofclaim 3, wherein a value of the variable threshold is further set basedon an acceptable false alarm rate.
 5. The method of claim 1, whereincollecting wireless channel information comprises the receiverestimating a probability distribution σ₀ through a training sequencewhere a number of packets used for training is denoted by N_(T) andcomputing a likelihood ratio L(h) for packets h=[h_(j), K, h_(k)] forj=i−N+1 where N=k−j+1 is a block size and k=i based on channel estimatesat each instant i (N≤i≤N_(T)) for each packet transmission.
 6. Themethod of claim 5, further comprising the receiver selecting, based onL(h) computed during a training phase, a threshold γ such that an alarmis raised whenever L(h)>γ.
 7. The method of claim 6, wherein in theevent of an alarm, a re-authentication procedure is evoked to reverifyan identity of the transmitter.
 8. The method of claim 5, wherein for asingle antenna mode:${L(h)} = {{\left( \frac{2N\;\sigma_{0}^{2}}{\lambda} \right)^{N}e^{({\frac{\lambda}{2\;\sigma_{0}^{2}} - N})}\mspace{14mu}{where}\mspace{14mu}\lambda} = {\sum\limits_{i = j}^{k}{h_{i}^{2}.}}}$9. The method of claim 5, wherein for multiple antenna modes:${L(h)} = {\sum\limits_{m = 1}^{M}\left\lbrack {\left( \frac{2N\;\sigma_{0\; m}^{2}}{\lambda_{m}} \right)^{N}e^{({\frac{\lambda}{2\;\sigma_{0m}^{2}} - N})}} \right\rbrack}$where λ_(m)=Σ_(i=j) ^(k)h_(im) ² and h_(im) denotes a channelrealization at time instant i for an m^(th) antenna mode.
 10. The methodof claim 1, wherein the antenna modes are selected such that patterncorrelation coefficients between different antenna modes are kept as lowas possible.